1. Melt the butter, blend in the flour, place over low heat and add milk slowly. Stir until thickened.
2. Blend in the cheese.
3. Beat the egg yolk until creamy, then stir into the thick sauce.
4. Add the rice, salt and pepper. Spread out on a platter and chill.
5. Set the frying kettle on a warm, not hot, part of the range. Fill it half full with shortening or other fat. Let it slowly heat to 370° F., or until a 1-inch cube of bread browns 40 seconds to 1 minute.
6. When the rice mixture is firm, shape it into small croquettes. Dip each in beaten egg white and roll in crumbs. Fry in the fat until delicately browned. Remove and drain on paper towels.